Mathematics Exam > Mathematics Questions > If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then...
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If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x| then the set of point of non-differentiability is,
- a){1,0,2}
- b){1,2}
- c){2}
- d){0,2}
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-...
Clearly the rule of the function is changing of x = 1 and 2.
So we shall test the differentiability of f(x) only at the points x = 1 and x = 2.
clearly Rf '(1) - Lf'(1)
and Rf*(2) ≠ Lf'(2)
hence f(x) is not differentiable at x = 2.
Most Upvoted Answer
If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-...
Point of Non-Differentiability for f(x) = (x^2 - 1) |x^2 - 3x + 2| + cos|x|
- Finding the Points of Non-Differentiability
To find the points of non-differentiability for the given function f(x), we need to consider the points where the function is not differentiable.
- Breakdown of the Function
The given function f(x) consists of three parts:
1. (x^2 - 1)
2. |x^2 - 3x + 2|
3. cos|x|
- Examining Each Part
1. The function (x^2 - 1) is a polynomial function and is differentiable for all real numbers.
2. The absolute value function |x^2 - 3x + 2| will change its behavior at the roots of the expression inside the absolute value.
Solving x^2 - 3x + 2 = 0 gives x = 1 and x = 2. Therefore, the function is non-differentiable at x = 1 and x = 2.
3. The cosine function cos|x| is continuous and differentiable for all real numbers.
- Conclusion
Therefore, the points of non-differentiability for the function f(x) = (x^2 - 1) |x^2 - 3x + 2| + cos|x| are x = 1 and x = 2. Hence, the correct answer is option 'c) {2}'.
- Finding the Points of Non-Differentiability
To find the points of non-differentiability for the given function f(x), we need to consider the points where the function is not differentiable.
- Breakdown of the Function
The given function f(x) consists of three parts:
1. (x^2 - 1)
2. |x^2 - 3x + 2|
3. cos|x|
- Examining Each Part
1. The function (x^2 - 1) is a polynomial function and is differentiable for all real numbers.
2. The absolute value function |x^2 - 3x + 2| will change its behavior at the roots of the expression inside the absolute value.
Solving x^2 - 3x + 2 = 0 gives x = 1 and x = 2. Therefore, the function is non-differentiable at x = 1 and x = 2.
3. The cosine function cos|x| is continuous and differentiable for all real numbers.
- Conclusion
Therefore, the points of non-differentiability for the function f(x) = (x^2 - 1) |x^2 - 3x + 2| + cos|x| are x = 1 and x = 2. Hence, the correct answer is option 'c) {2}'.
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Community Answer
If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-...
Clearly the rule of the function is changing of x = 1 and 2.
So we shall test the differentiability of f(x) only at the points x = 1 and x = 2.
clearly Rf '(1) - Lf'(1)
and Rf*(2) ≠ Lf'(2)
hence f(x) is not differentiable at x = 2.
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If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer?.
If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) = (x2 - 1) |x2 - 3x + 2| + cos|x|then the set of point of non-differentiability is,a){1,0,2}b){1,2}c){2}d){0,2}Correct answer is option 'C'. Can you explain this answer?.
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